Random walk and non-Gaussianity of the 3D second-quantized Schrödinger–Newton nonlocal soliton

Abstract

Nonlocal quantum fluids emerge as dark-matter models and tools for quantum simulations and technologies. However, strongly nonlinear regimes, like those involving multi-dimensional self-localized solitary waves, are marginally explored for what concerns quantum features. We study the dynamics of 3D+1 solitons in the second-quantized nonlocal nonlinear Schroedinger-Newton equation. We theoretically investigate the quantum diffusion of the soliton center of mass and other parameters, varying the interaction length. 3D+1 simulations of the Ito partial differential equations arising from the positive P-representation of the density matrix validate the theoretical analysis. The numerical results unveil the onset of non-Gaussian statistics of the soliton, which may signal quantum-gravitational effects and be a resource for quantum computing. The non-Gaussianity arises from the interplay between the soliton parameter quantum diffusion and stable invariant propagation. The fluctuations and the non-Gaussianity are universal effects expected for any nonlocality and dimensionality.

Dark matter condensates as highly nonlocal solitons: instability in the Schwarzschild metric and laboratory analog

“…Our model is not only a simple closed-form analysis of the interaction of DM with BH but suggests simulating the physics of DM interaction with a curved spacetime in the laboratory by time-varying traps. This may open the way to study first and second quantized DM dynamics [25,26] in simulated gravity with atoms, polaritons, and optical systems [27][28][29].…”